An analysis of airport–airline vertical relationships with risk sharing contracts under asymmetric information structures

• We analyze the double moral hazard problem of airport–airline vertical risk-sharing relationship.
• Two parties both make efforts but neither of them can see the other’s efforts.
• Our continuous stochastic dynamic model shows they agree on an optimal linear contract.
• Its slope is a product of their productivity difference and uncertainty level index.
• Complex impacts of environmental parameters are presented in numerical examples.

We analyze the double moral hazard problem at the joint venture type airport–airline vertical relationship, where two parties both contribute efforts to the joint venture but neither of them can see the other’s efforts. With the continuous-time stochastic dynamic programming model, we show that by the de-centralized utility maximizations of two parties under very strict conditions, i.e., optimal efforts’ cost being negligible and their risk averse parameters both asymptotically approaching to zero, the vertical contract could be agreed as the optimal sharing rule, which is the linear function of the final state with the slope being the product of their productivity difference and uncertainty (diffusion rate) level index.If both parties’ productivities are same, or the diffusion rate of the underlying process is unity, optimal linear sharing rule do not depend on the final state. If their conditions not dependent on final state are symmetric as well, then risk sharing disappears completely. In numerical examples, we illustrate the complex impact of uncertainty increase and end-of-period load factor improvement on the optimal sharing rule, and the relatively simple impact on total utility levels.